text: Molecules made up of elements with multiple isotopes can vary in their isotopic composition, these different mass molecules are called isotopologues. Isotopologues such as COO, contain multiple heavy isotopes of oxygen substituting for the more common O, and are termed multiply-substituted isotopologues. The multiply-substituted isotopologue COO contains a bond between two of these heavier isotopes (C and O), which is a "clumped" isotope bond. 
  The abundance of masses for a given molecule (e.g. CO) can be predicted using the relative abundance of isotopes of its constituent atoms (C/C, O/O and  O/O). The relative abundance of each isotopologue (e.g. mass-47 CO) is proportional to the relative abundance of each isotopic species. 
  This predicted abundance assumes a non-biased stochastic distribution of isotopes, natural materials tend to deviate from these stochastic values, the study of which forms the basis of clumped isotope geochemistry. 
  When a heavier isotope substitutes for a lighter isotope (e.g., O for O), the chemical bond's vibration will be slower, lowering its zero-point energy. In other words, thermodynamic stability is related to the isotopic composition of the molecule.
  CO  (≈98.2%), CO (≈1.1%), COO (≈0.6%) and COO (≈0.11%) are the most abundant isotopologues (≈99%) for the carbonate ions, controlling the bulk δC, δO and δO values in natural carbonate minerals. Each of these isopotologes has different thermodynamic stability. For a carbonate crystal at thermodynamic equilibrium, the relative abundances of the carbonate ion isotopologues is controlled by reactions such as:
  The equilibrium constants for these reactions are temperature-dependent, with a tendency for heavy isotopes to "clump" with each other (increasing the proportions of multiply substituted isotopologues) as temperature decreases. Reaction 1 will be driven to the right with decreasing temperature, to the left with increasing temperature. Therefore, the equilibrium constant for this reaction can be used as an paleotemperature indicator, as long as the temperature dependence of this reaction and the relative abundances of the carbonate ion isotopologues are known.